import numpy as np
import matplotlib.pyplot as plt
import math
from basic import *


x = list(range(3, 20))

y = [math.factorial(i) for i in x]
y1 = [i*(i-1) for i in x]
y2 = [i*(i-1)*(i-2)*(i-3) for i in x]
y3 = [i*(i-1)*(i-2)*(i-3)*(i-4)*(i-5) for i in x]

plt.axes(yscale="log")
plt.plot(x, y, label="STE")
plt.plot(x, y1, label="$t=1$")
plt.plot(x, y2, label="$t=2$")
plt.plot(x, y3, label="$t=3$")
plt.xlabel('$m$')
plt.ylabel('Permutations')
plt.legend()
plt.tight_layout()
plt.savefig(PATH+'functions.pdf', format='pdf')
plt.show()